Abstract One of the most fundamental challenges facing scientists and engineers across different fields, such as computer vision, robotics, bioinformatics and image processing, is the large amounts of high-dimensional data that need to be analyzed and understood. In this talk, I present provably correct and efficient algorithms, based on the sparse representation theory, for the analysis of high-dimensional datasets by exploiting their underlying low-dimensional structures. I talk about algorithms for the two fundamental problems of clustering and subset selection in unions of subspaces and...